Class 11 Mathematics Straight Lines MCQs Set D

Question. If the three lines x – 3y = p, ax + 2y = q and ax + y = r form a right-angled triangle then :
(a) a² – 9a + 18 = 0
(b) a² – 6a – 12 = 0
(c) a² – 6a – 18 = 0
(d) a² – 9a + 12 = 0
Answer: a

Question. A straight line through the point A (3, 4) is such that its intercept between the axes is bisected at A. Its equation is
(a) x + y = 7
(b) 3x – 4y + 7 = 0
(c) 4x + 3y = 24
(d) 3x + 4y = 25
Answer: c

Question. If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals :
(a) 35/3
(b) –5
(c) – 35/3
(d) 5
Answer: d

Question. The point of intersection of the lines (α³ + 3)x + αy + α – 3 = 0 and (α⁵ + 2)x + (α + 2)y + 2α + 3 = 0 (a real) lies on the y-axis for
(a) no value of α
(b) more than two values of α
(c) exactly one value of α
(d) exactly two values of α
Answer: a

Question. If a line with slope m makes x-intercept d. Then equation of the line is :
(a) y = m(d – x)
(b) y = m(x – d)
(c) y = m(x + d)
(d) y = mx + d
Answer: b

Question. Let a, b, c and d be non- ero numbers. If the point of intersection of the lines 4ax + 2ay + c = 0 and 5bx + 2by + d = 0 lies in the fourth quadrant and is equidistant from the two axes then
(a) 3bc – 2ad = 0
(b) 3bc + 2ad = 0
(c) 2bc – 3ad = 0
(d) 2bc + 3ad = 0
Answer: a

Question. If the three distinct lines x + 2ay + a = 0, x + 3by + b = 0 and x + 4ay + a = 0 are concurrent, then the point (a, b) lies on a:
(a) circle
(b) hyperbola
(c) straight line
(d) parabola
Answer: c

Question. The equation of a straight line passing through (–3, 2) and cutting an intercept equal in magnitude but opposite in sign from the axes is given by
(a) x – y + 5 = 0
(b) x + y – 5 = 0
(c) x – y – 5 = 0
(d) x + y + 5 = 0
Answer: a

Question. If one of the lines of my² + (1– m²) xy – mx²= 0 is a bisector of the angle between the lines xy = 0, then m is
(a) 1
(b) 2
(c) –1/2
(d) –2
Answer: a

Question. If the sum of the slopes of the lines given by x² – 2cxy – 7y² = 0 is four times their product c has the value
(a) –2
(b) –1
(c) 2
(d) 1
Answer: c

Question. The relation between a, b, a’ and b’ such that the two lines ax + by = c and a’x + b’y = c’ are perpendicular is
(a) aa’ – bb’ = 0
(b) aa’ + bb’ = 0
(c) ab + a’b’ = 0
(d) ab – a’b’ = 0
Answer: b

Question. If the extremities of the base of an isosceles triangle are the points (2a, 0) and (0, a) and the equation of one of the sides is x = 2a, then the area of the triangle, in square units, is :
(a) (5/4)a²
(b) (5/2)a²
(c) 25a²/4
(d) 5a²
Answer: b

Question. The base of an equilateral triangle is along the line given by 3x + 4y = 9. If a vertex of the triangle is (1, 2), then the length of a side of the triangle is:
(a) 2√3/15
(b) 4√3/15
(c) 4√3/5
(d) 2√3/5
Answer: b

Question. If p be the length of the perpendicular from the origin on the straight line x + 2by = 2p ,then what is the value of b?
(a) 1/p
(b) p
(c) 1/2
(d) √3/2
Answer: d

Question. Reduce the equation √3x + y−8 =0 into normal form. The value of p is
(a) 2
(b) 3
(c) 4
(d) 5
Answer: c

Question. The lines p(p² +1)x – y + q = 0 and (p² + 1)²x + (p² + 1)y + 2q = 0 are perpendicular to a common line for :
(a) exactly one values of p
(b) exactly two values of p
(c) more than two values of p
(d) no value of p
Answer: a

Question. The shortest distance between the line y – x = 1 and the curve x = y² is :
(a) 2√3/8
(b) 3√2/5
(c) √3/4
(d) 3√2/8
Answer: d

Question. If the pair of straight lines x² – pxy – y² = 0 and x² – 2qxy – y² = 0 be such that each pair bisects the angle between the other pair, then
(a) pq = –1
(b) p = q
(c) p = –q
(d) pq = 1
Answer: a

Question. The straight lines x + 2y – 9 = 0, 3x + 5y – 5 = 0 and ax + by = 1 are concurrent if the straight line 35x – 22y + 1 = 0 passes through :
(a) (a, b)
(b) (b, a)
(c) (a, – b)
(d) (– a, b)
Answer: a

Question. Locus of mid point of the portion between the axes of x cosα + y sinα = p whre p is constant is
(a) x² + y² = 4/p²
(b) x² + y² = 4p²
(c) 1/x² + 1/y² = 2/p²
(d) 1/x² + 1/y² = 4/p²
Answer: d

Question. Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, – 4) in this line is:
(a) (11/5, 28/5)
(b) (29/5, 8/5)
(c) (8/5, 29/5)
(d) (29/5, 11/5)
Answer: a

Question. If the x-intercept of some line L is double as that of the line, 3x + 4y = 12 and the y-intercept of L is half as that of the same line, then the slope of L is :
(a) – 3
(b) – 3/8
(c) – 3/2
(d) – 3/16
Answer: d

Question. If the image of point P(2, 3) in a line L is Q(4, 5), then the image of point R(0, 0) in the same line is:
(a) (2, 2)
(b) (4, 5)
(c) (3, 4)
(d) (7, 7)
Answer: d

Question. The perpendicular from the origin to the line y = mx + c meets it at the point (–1, 2). Find the value of m + c. 
(a) 2
(b) 3
(c) 4
(d) 5
Answer: b

Question. A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two ad acent vertices of the rectangle are (–8, 5) and (6, 5), then the area of the rectangle (in sq. units) is:
(a) 84
(b) 98
(c) 72
(d) 56
Answer: a

Question. The vertices of a triangle ABC are (1, 1), (4, – 2) and (5, 5) respectively. Then equation of perpendicular dropped from C to the internal bisector of angle A is
(a) y – 5 = 0
(b) x – 5 = 0
(c) 2x + 3y –7 = 0
(d) None of these
Answer: b

Question. The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 is:
(a) 3/2
(b) 3/10
(c) 6
(d) 9/4
Answer: b

Question. Value of x so that 2 is the slope of the line through (2, 5) and (x, 3) is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: b

Question. The equation y = sin x sin (x + 2) – sin² (x + 1) represents a straight line lying in :
(a) second and third quadrants only
(b) first, second and fourth quadrant
(c) first, third and fourth quadrants
(d) third and fourth quadrants only
Answer: d

Question. Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?
(a) The lines are concurrent at the point (3/4, 1/2)
(b) Each line passes through the origin.
(c) The lines are all parallel.
(d) The lines are not concurrent.
Answer: a

Question. Let the equations of two sides of a triangle be 3x – 2y + 6 = 0 and 4x + 5y – 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is:
(a) 122y – 26x – 1675 = 0
(b) 122y + 26x + 1675 = 0
(c) 26x + 61y + 1675 = 0
(d) 26x – 122y – 1675 = 0
Answer: d

Question. If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square, then the equation of second diagonal is
(a) x + 3y = 21
(b) 2x – 3y = 7
(c) x + 7y = 31
(d) 2x + 3y = 21
Answer: c

Question. Choose the correct statement which describe the position of the point (–6, 2) relative to straight lines 2x + 3y – 4 = 0 and 6x + 9y + 8 = 0.
(a) Below both the lines
(b) Above both the lines
(c) In between the lines
(d) None of these
Answer: a

Question. If the mid-point of the section of a straight line intercepted between the axes is (1, 1), then what is the equation of this line?
(a) 2x + y = 3
(b) 2x – y = 1
(c) x – y = 0
(d) x + y = 2
Answer: d

Question. Two sides of a parallelogram are along the lines, x + y = 3 and x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is:
(a) (3, 5)
(b) (2, 1)
(c) (2, 6)
(d) (3, 6)
Answer: d

Question. The foot of the perpendicular drawn from the origin, on the line, 3x + y = l(l ¹ 0) is P. If the line meets x-axis at A and y-axis at B, then the ratio BP : PA is
(a) 9 : 1
(b) 1 : 3
(c) 1 : 9
(d) 3 : 1
Answer: d

Question. The sides of a rhombus ABCD are parallel to the lines, x – y + 2 = 0 and 7x – y + 3 = 0. If the diagonals of the rhombus intersect at P(1, 2) and the vertex A (different from the origin) is on the y-axis, then the ordinate of A is
(a) 2
(b) 7/4
(c) 7/2
(d) 5/2
Answer: d

Question. The points A(1, 3) and C(5, 1) are the opposite vertices of rectangle. The equation of line passing through other two vertices and of gradient 2, is
(a) 2x + y – 8 = 0
(b) 2x – y – 4 = 0
(c) 2x – y + 4 = 0
(d) 2x + y + 7 = 0
Answer: b

Question. The reflection of the point (4, – 13) in the line 5x + y + 6 = 0 is
(a) (–1, –14)
(b) (3, 4)
(c) (0, 0)
(d) (1, 2)
Answer: a

Question. The inclination of the line x – y + 3 = 0 with the positive direction of x-axis is
(a) 45°
(b) 135°
(c) –45°
(d) –135°
Answer: a